We've kicked around a number of systems like this, but they're all too vulnerable to collusion, botting, or fluff. The real test of a system that solves these problems would be how it handles players who only roleplay enough to satisfy the local rules. Some goals, restricting myself to fully automated solutions:

1) It shouldn't reward someone for inflicting themselves on others, and simply talking the most. As an example, you might consider tracking when someone is "in a conversation" (i.e. they are talking, someone else is talking, they can mutually hear one another, etc.), and basing the rewards more on the duration of participation rather than number of words or lines said.

2) It should automatically frustrate simple attempts at automation. Maybe you track the last N things a person said, and discard duplicates. Of course, a malicious player could write a bot of the form "Choose a subject from list A and a predicate from list B" and overwhelm such a system fairly trivially, but they'd still have to have collusion (or multiple characters on simultaneously, which most RP-required games forbid) to make it worthwhile.

3) You should automatically log all qualifying speech (at least temporarily) so that alleged abuse can be verified. It's probably also useful to track total RPXP received, and have an easy way to parse who is getting the most. (I disagree strongly with Molly that snooping IC channels is an invasion of privacy, especially on a MUD where roleplaying is required. If you can't or don't snoop, you can't tell if your rules are being followed.)

4) Collusion is another obvious problem. One solution might be diminishing returns- the more you talk with Player A, the less RPXP/time-unit you get. This unfortunately discourages deep long-term plots involving a few key parties, but it also makes collusion unprofitable, and provides an incentive to avoid cliques, since the optimal strategy would be to frequently change conversational partners.

Even with all of the above, the system has two huge flaws:
A) Automated code cannot discern quality of speech. It rewards raw time/effort over skill.
B) Actions are every bit as important as words. A brave knight who enters battle even though hopelessly outnumbers may well be roleplaying perfectly even though he never says a word beyond a quick battle shout.

Frankly, I think the drawbacks overwhelm any benefit the system might bring. It might be useful more as a tracking system then a reward system per se. In other words, count up RPXP, use it for figuring out which PCs are putting in effort, and couple that to "manual" roleplay rewards such as staff members handing out subjective bonuses, or starting quests through those characters.